The phase model enables us to perform a detailed analysis of synchronization due to interactions among elements in a network.
To analyze synchronization dynamics only with given times-series data, estimation of the phase model (REF ) from data has been discussed [1]}, [2]}, [3]}, [4]}.
In these existing methods, to obtain the phase model (REF ), the phase variable \(\theta _i\)  is first estimated by, for example, the linear interpolation or the Hilbert transform [1]}, [2]}.
Then, the PCF \(\Gamma _i\)  is estimated, for example, by fitting the data to the Fourier series [3]}, [4]}, by using kernel density estimation [1]}, or by using dynamic Bayesian inference [2]}.
